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The main purpose of this work is to present recent results obtained on the existence of Fxed points for nonexpansive mappings and orbit-nonexpansive mappings in the general context of metric spaces. Additionally, our tech- niques will allow us to deduce the existence of common xed points for groups of such mappings based on features of the closed balls of the metric space. In order to do that, the concepts of normal structure and uniform normal structure will be analyzed and extended from the Banach space framework to the more general environment of metric spaces. Applications to important families of metric spaces without linear structure will be dis- played. The work is divided into three chapters which are subdivided into sec- tions. In Chapter 1 we present the basic concepts and results that we believe are necessary for reading and understanding the other chapters. In Chapter 2 and Chapter 3 we present the aforemetioned results most of which can be found in the articles [1] and [2] by Rafael Espínola García, María Japón and myself.

This article addresses reflections on the conception of heritage used in our society, articulating the theme with the concept of decoloniality, based on the study of Gravataí, a city in the metropolitan region of Porto Alegre, Rio Grande do Sul. The municipality has its origin marked by the occupation of indigenous peoples, followed by a process of expulsion, expanding the Portuguese community, which brought with it enslaved people of African origin. However, the processes of patrimonialization of municipal assets have as ballast the exaltation of the Portuguese heritage and the seal of an authorized discourse of heritage, which legitimizes a hegemonic perspective on the past. This situation makes it possible to question the possibility of a decolonial heritage within the Brazilian context., Este artigo aborda reflexões acerca da concepção de patrimônio utilizada em nossa sociedade, articulando o tema com o conceito de decolonialidade, a partir do estudo de Gravataí, cidade da região metropolitana de Porto Alegre, Rio Grande do Sul. O munícipio tem sua origem marcada pela ocupação de povos indígenas, seguida por um processo de expulsão, ampliando a comunidade lusitana, que trouxe consigo pessoas escravizadas de origem africana. Todavia, os processos de patrimonialização dos bens municipais têm como lastro o enaltecimento da herança portuguesa e a chancela de um discurso autorizado do patrimônio, que legitima uma perspectiva hegemônica sobre o passado. Tal conjuntura torna-se propícia para questionar a possibilidade de um patrimônio decolonial dentro do contexto brasileiro.

The pandemic brought changes in various human spaces and activities, including sport. By involving voluminous financial sums, especially when we think about the sport spectacles of the main leagues on the planet, sport seems to us to have been the most “trivial” of the activities seeking to resist the changes in biological and economic risk that characterized the pandemic, with elite sports, although many disagreed, practically surviving as an essential activity. However, to surpass such obstacles, changes and adaptations proved necessary. In this essay, we use the proposal Analytical Model of the 5 E’s to understand, from a comprehensive perspective of the proposed dimensions, what were the main changes that affected sport in a historical moment in which health and disease have taken center stage in our lives. We noticed changes in sports consumption, supply and demand relationships, behavioral and emotional changes in athletes and spectators, as well as health issues. Sport, as a “non-essential” activity, adapted itself to the new “normal,” driven by mercantile and spectacularization mechanisms., La pandemia ha traído cambios en diversos espacios y actividades humanas, incluido el deporte. Al involucrar voluminosas sumas económicas, especialmente cuando pensamos en los espectáculos deportivos de las principales ligas del planeta, el deporte nos parece haber sido la más “banal” de las actividades que buscaban resistir los cambios de riesgo biológico y económico que caracterizaron la pandemia, con el deporte de alto rendimiento, aunque muchos no estaban de acuerdo, sobreviviendo prácticamente como actividad imprescindible. Sin embargo, para sobrevivir a tales obstáculos, los cambios y las adaptaciones resultaron necesarios. En este ensayo, utilizamos la propuesta del Modelo Analítico de las 5 E's para comprender, desde una perspectiva integral de las dimensiones propuestas, cuáles fueron los principales cambios que afectaron al deporte en un momento histórico en el que la salud y la enfermedad han ocupado un lugar central en nuestras vidas. Se notaron cambios en el consumo deportivo, relaciones de oferta y demanda, en los comportamientos y emociones de los atletas y espectadores, así como el cuidado de la salud corporal. El deporte, como “actividad no esencial”, se adaptó rápidamente a la nueva “normalidad”, impulsado por mecanismos de mercantilización y espectáculo.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the agent of a major global outbreak of respiratory tract disease known as Coronavirus Disease 2019 (COVID-19). SARS-CoV-2 infects mainly lungs and may cause several immune-related complications, such as lymphocytopenia and cytokine storm, which are associated with the severity of the disease and predict mortality. The mechanism by which SARS-CoV-2 infection may result in immune system dysfunction is still not fully understood. Here, we show that SARS-CoV-2 infects human CD4+ T helper cells, but not CD8+ T cells, and is present in blood and bronchoalveolar lavage T helper cells of severe COVID-19 patients. We demonstrated that SARS-CoV-2 spike glycoprotein (S) directly binds to the CD4 molecule, which in turn mediates the entry of SARS-CoV-2 in T helper cells. This leads to impaired CD4 T cell function and may cause cell death. SARS-CoV-2-infected T helper cells express higher levels of IL-10, which is associated with viral persistence and disease severity. Thus, CD4-mediated SARS-CoV-2 infection of T helper cells may contribute to a poor immune response in COVID-19 patients.

Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables designed to summarise the data. In practice however, for large datasets requiring many inducing variables, such as low-lengthscale spatial data, even sparse GPs can become computationally expensive, limited by the number of inducing variables one can use. In this work, we propose a new class of inter-domain variational GP, constructed by projecting a GP onto a set of compactly supported B-spline basis functions. The key benefit of our approach is that the compact support of the B-spline basis functions admits the use of sparse linear algebra to significantly speed up matrix operations and drastically reduce the memory footprint. This allows us to very efficiently model fast-varying spatial phenomena with tens of thousands of inducing variables, where previous approaches failed., Comment: 14 pages, 5 figures, published in AISTATS 2023

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting an appropriate kernel can be challenging. Deep GPs avoid manual kernel engineering by successively parameterizing kernels with GP layers, allowing them to learn low-dimensional embeddings of the inputs that explain the output data. Following the architecture of deep neural networks, the most common deep GPs warp the input space layer-by-layer but lose all the interpretability of shallow GPs. An alternative construction is to successively parameterize the lengthscale of a kernel, improving the interpretability but ultimately giving away the notion of learning lower-dimensional embeddings. Unfortunately, both methods are susceptible to particular pathologies which may hinder fitting and limit their interpretability. This work proposes a novel synthesis of both previous approaches: Thin and Deep GP (TDGP). Each TDGP layer defines locally linear transformations of the original input data maintaining the concept of latent embeddings while also retaining the interpretation of lengthscales of a kernel. Moreover, unlike the prior solutions, TDGP induces non-pathological manifolds that admit learning lower-dimensional representations. We show with theoretical and experimental results that i) TDGP is, unlike previous models, tailored to specifically discover lower-dimensional manifolds in the input data, ii) TDGP behaves well when increasing the number of layers, and iii) TDGP performs well in standard benchmark datasets., Comment: Accepted at the Conference on Neural Information Processing Systems (NeurIPS) 2023